The axial instability of the winding conductor is one of the principal modes of mechanical failure in large power transformers. It is caused by axial compressive forces generated by the electromagnetic interaction of the short-circuit current and the radial leakage flux. It is a buckling type of mechanical instability that occurs under compression. Two possible modes of failure in the layer type coil wound with the continuously transposed cable are identified and analyzed in this paper. The critical design loads leading to instability of the individual strands as well as of the whole cable are separately derived. The actual instability threshold of the coil would be the lesser of the two critical loads. For the through-fault integrity of the transformer design, this threshold must be greater than the peak compressive force on the cable under the worst case short-circuit current